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A035841 Coordination sequence for A_15 lattice.

%I A035841 #19 Jul 01 2018 05:57:20
%S A035841 1,240,14520,400080,6447660,70006512,561075720,3536846160,18363363690,
%T A035841 81289041680,315029394792,1091144804400,3433533723900,9946019437200,
%U A035841 26808012135000,67830161708592,162298598439330,369504358622640,804648531335960,1683493452034320
%N A035841 Coordination sequence for A_15 lattice.
%H A035841 Colin Barker, <a href="/A035841/b035841.txt">Table of n, a(n) for n = 0..1000</a>
%H A035841 R. Bacher, P. de la Harpe and B. Venkov, <a href="http://dx.doi.org/10.1016/S0764-4442(97)83542-2">Séries de croissance et séries d'Ehrhart associées aux réseaux de racines</a>, C. R. Acad. Sci. Paris, 325 (Series 1) (1997), 1137-1142.
%H A035841 J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (<a href="http://neilsloane.com/doc/Me220.pdf">pdf</a>).
%H A035841 Joan Serra-Sagrista, <a href="http://dx.doi.org/10.1016/S0020-0190(00)00119-8">Enumeration of lattice points in l_1 norm</a>, Inf. Proc. Lett. 76 (1-2) (2000) 39-44.
%H A035841 <a href="/index/Rec#order_15">Index entries for linear recurrences with constant coefficients</a>, signature (15, -105, 455, -1365, 3003, -5005, 6435, -6435, 5005, -3003, 1365, -455, 105, -15, 1).
%F A035841 Sum_{d=1..15} C(16, d)*C(m/2-1, d-1)*C(15-d+m/2, m/2), where norm m is always even.
%F A035841 G.f.: -(x+1)*(x^14 + 224*x^13 + 10801*x^12 + 196224*x^11 + 1667001*x^10 + 7351008*x^9 + 17699017*x^8 + 23710208*x^7 + 17699017*x^6 + 7351008*x^5 + 1667001*x^4 + 196224*x^3 + 10801*x^2 + 224*x + 1) / (x-1)^15. - _Colin Barker_, Mar 03 2015
%o A035841 (PARI) Vec(-(x +1)*(x^14 +224*x^13 +10801*x^12 +196224*x^11 +1667001*x^10 +7351008*x^9 +17699017*x^8 +23710208*x^7 +17699017*x^6 +7351008*x^5 +1667001*x^4 +196224*x^3 +10801*x^2 +224*x +1) / (x -1)^15 + O(x^100)) \\ _Colin Barker_, Mar 03 2015
%K A035841 nonn,easy
%O A035841 0,2
%A A035841 Joan Serra-Sagrista (jserra(AT)ccd.uab.es)